To fill the bit about using iTunes on a computer.
Basically you can sync a folder, or a folder of folders from your PC (the secondary folders become albums, one level only). All rearrangement of photos synced this way must be done in the folders on the PC (or Mac) and then re-synced before changes happen on the iPad.
iTunes: Syncing photos
Most people who want to manage mange photo albums on the iPad end up getting a third party app like Photo Manager Pro. There are dozens of these app, many of which are specialized for particular needs; family photo albums, professional portfolios, etc.
Another option: If you have iCloud and don't mind a little extra work, you can use Shared Photo Streams to create albums. You don't have to actually share them. Unlike the basic Photo Stream, these albums are not temporary, and they will sync between all devices that use the same iCloud account (and have Shared Photo Stream turned on).
Since you are actually creating copies for the shared albums, you'll need to delete photos from the camera roll (or imported album) after you've placed them in the shared album. That's the extra work.
The main advantage of doing it this way is that the photos remain available to other apps for emailing, sharing, including in documents, etc. Photos that are in a third party photo management app need to be copied back to the Camera Roll in the Photos app before they can be used by other apps.
Photo Stream FAQ
iCloud: My Photo Stream FAQ
Shared Photo Stream FAQ
iCloud: Shared Photo Streams FAQ
While Shared Photo Streams are permanent, well, as permanent as any online account, I do not recommend trusting important photos solely to iCloud. Actually, I don't recommend trusting any file to just one place or device, especially to a mobile device. Be sure you make a habit of saving all your photos to another computer or a second online photo site; both for the ones you really don't want to lose.
Good luck.